Extraordinary Hall effect in Fe-Cr giant magnetoresistive multilayers

We show that for giant magnetoresistive Fe-Cr multilayer samples, the scaling law for the extraordinary Hall constant, RS~ρⁿ gives unrealistically large values of $n(n=2.8--3.3)$ if we use the resistivity ρ at an external field $B=0$ as done by previous investigators. With B perpendicular to the film plane, the transverse magnetoresistance saturates at B≈3 T in the 4.2--300 K temperature range. This indicates that the Fe layers, although antiferromagnetically coupled at $B=0,$ are ferromagnetically aligned only above B≈3 T. Therefore, we use ρ=ρ(B=3T) in RS~ρⁿ and obtain n=1.96±0.02, which implies that the side-jump mechanism $n=2$ is the dominant scattering process. We emphasize that our interpretation of RS(ρ) not only evolves from a proper understanding of the magnetic state of the multilayer system but also yields physically meaningful values of the exponent n.